Solving Equations with Fractions

This video tutorial explains how to solve the equation x/7 + y/9 = 1 using two methods: clearing fractions and solving with fractions. It begins by introducing the equation and discussing the choice between solving with or without fractions. The first method involves clearing fractions by multiplying both sides by the least common denominator, simplifying, and isolating y. The second method keeps fractions in the equation, isolating y by subtracting terms and multiplying to solve. Both methods are shown to yield equivalent expressions for y, demonstrating different approaches to the same problem.

What is the first step in deciding how to solve the equation x/7 + y/9 = 1?

• Multiply both sides by 7.

• Determine if you want to solve for x first.

• Add 9 to both sides.

• Decide whether to clear fractions or not.

What is the least common multiple of 9 and 7 used to clear fractions?

• 81

• 49

• 63

• 56

After clearing fractions, what is the expression for y in terms of x?

• y = (9x - 63) / 7

• y = (9x + 63) / 7

• y = (63 - 9x) / 7

• y = (63 + 9x) / 7

How can the expression y = (63 - 9x) / 7 be rewritten?

• y = 9 - (9/7)x

• y = 9 + (9/7)x

• y = 7 - (9/7)x

• y = 7 + (9/7)x

What is the first step when solving the equation without clearing fractions?

• Multiply both sides by 9.

• Add x/7 to both sides.

• Subtract x/7 from both sides.

• Divide both sides by 9.

What operation is used to isolate y when solving without clearing fractions?

• Addition

• Subtraction

• Multiplication

• Division

How can y be expressed after solving without clearing fractions?

• y = 9 + (x/7)

• y = 9 - (x/7)

• y = 9 * (1 - x/7)

• y = 9 / (1 - x/7)

What is the equivalent expression for y = 9 * (1 - x/7)?

• y = 9 - (9/7)x

• y = 9 + (9/7)x

• y = 9 - (7/9)x

• y = 9 + (7/9)x

Why is it important to recognize equivalent expressions for y?

• To understand different forms of the solution.

• To simplify the equation further.

• To solve for x more easily.

• To verify the solution is correct.

What is the final expression for y after solving the equation?

• y = 7 + (9/7)x

• y = 9 - (9/7)x

• y = 9 + (9/7)x

• y = 7 - (9/7)x